Permutations And Combinations

Step 1: Understanding the problem.
We are asked to find the rank of the word "CEBADA" when all the permutations of the letters of this word are listed alphabetically.
Step 2: Finding the rank.
The word CEBADA consists of 6 letters: C, E, B, A, D, A.
- The total number of permutations of the letters is because the letter A repeats twice. This gives us 360 total permutations.
- We need to count how many words come before "CEBADA" alphabetically. The first step is to arrange the letters in alphabetical order: A, B, C, D, E.
- Words starting with "A" or "B" come before any word starting with "C," so we consider the number of such words. After calculating, we find the rank of "CEBADA" to be 245.
Step 3: Conclusion.
The correct answer is (B) 245, as this is the rank of the word "CEBADA" in alphabetical order.